Problem: Solve for $x$ and $y$ using elimination. ${5x-2y = 15}$ ${-4x+5y = 22}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $2$ ${25x-10y = 75}$ $-8x+10y = 44$ Add the top and bottom equations together. $17x = 119$ $\dfrac{17x}{{17}} = \dfrac{119}{{17}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {5x-2y = 15}\thinspace$ to find $y$ ${5}{(7)}{ - 2y = 15}$ $35-2y = 15$ $35{-35} - 2y = 15{-35}$ $-2y = -20$ $\dfrac{-2y}{{-2}} = \dfrac{-20}{{-2}}$ ${y = 10}$ You can also plug ${x = 7}$ into $\thinspace {-4x+5y = 22}\thinspace$ and get the same answer for $y$ : ${-4}{(7)}{ + 5y = 22}$ ${y = 10}$